I don’t think this is a cactus—I believe this succulent is a Euphorbia-- Euphorbia leucodendron. It’s commonly called “Cat Tails Euphorbia,” for obvious reasons. It’s a member of the spurge family, which has over 2000 members. Many of them resemble cacti, but they are actually not related. This type of euphorbia is referred to as coraliform, due to its graceful, slender, coral-like stems.
In the spring, small lime green leaves (cyathia) appear on the plant (I can see them on yours), and colorful red fruit. When they eventually fall off, they leave those dark raised bumps.
Some sources say that these plants are cold hardy to -3.9 °C (25 °F). It needs well-drained soil, is draught-tolerant, and prefers full sun. Here’s more information: http://homeguides.sfgate.com/euphorbia-leucodendron-80188.html
Source for sfgate article above:
- San Marcos Growers: Euphorbia Leucodendron
- Michigan State University: Euphorbia Leucodendron
- Washington State University Clark County Extension: Euphorbia
- North Carolina State University: Plants Poisonous to Livestock and Pets in North Carolina
- International Euphorbia Society: About Euphorbiaceae
- USDA: U.S. Department of Agriculture Plant Hardiness Zone Map